1. The Physical Significance of Time-Averaged Doppler Shifts Along Magnetic Polarity Inversion Lines (PILs) Brian Welsch Space Sciences Laboratory, UC-Berkeley

2. Main Ideas 0. The transport of magnetic flux across the photosphere – emergence & submergence – plays a key role in many types of solar activity. Filament formation (flux cancellation), CME/flare triggering, the global dynamo, time-dependent coronal magnetic field models. 1. Flux only emerges & submerges along polarity inversion lines (PILs), along which B n vanishes. Vertical velocities elsewhere either: (1) are siphon flows, or (2) transport photospheric flux, but do not add or remove it. 2. Near disk center, the time-averaged Doppler shift determines the normal velocity, v n, hence whether flux is emerging or submerging. This shift is hard to determine – line center is pseudo- red-shifted relative to non-magnetic Sun. 3. If the horizontal field B h is known, the rate of flux emergence/ submergence along PILs can be quantified, v n B h. Pilot study soon, then to a review panel near you… Collaborators welcome!

3. Why is it important to quantify the amount of flux that’s emerging & submerging? Filament formation: S. Martin (1998) calls flux cancellation “necessary” to form filaments – and filaments erupt! Is cancellation usually emergence, reconnection, or submergence? Flare / CME triggering: Case studies (e.g., Schrijver et al. 2008) and simulations (many by Manchester et al.) suggest flux emergence can trigger flares & CMEs Global Dynamo: ~3,000 ARs/cycle, ~10 22 Mx of flux/AR. All this flux must disappear from the photosphere somehow. How much of this flux goes back down (submerges)? Electric Fields for Data-Driven Simulations: E-fields can be estimated from sequences of magnetograms & Faraday’s Law,  t B = -c(  x E), but E is under-determined by the gradient of a scalar – except along polarity inversion lines (PILs) near disk center, where (ideally) E h = v z x B h /c.

4. What is flux cancellation? Phenomenologically, Martin & Livi defined it as the “mutual apparent loss of magnetic flux in closely- spaced features of opposite polarity” Physically, feature cancellation is the photospheric manifestation of (Zwaan): 1.Emergence of a U-loop. 2.Submergence of an inverted U-loop. 3.Reconnection-associated emergence and/or submergence – depending on height.

5. Emergence of a U-loop will lead to cancellation. L. van Driel-Gesztelyi, J.-M. Malherbe, & Demoulin, P., 2000: lack of coronal activity over cancellation site in MDI t 1 t 2 t 3

6. Submergence of an inverted U-loop will also lead to apparent cancellation. J. Chae, Y.- J. Moon, A. A. Pevtsov, 2004: Doppler shifts of ~1 km/s at cancellation site, with B t ~ 1 kG t 1 t 2 t 3

7. Reconnection-associated submergence will also lead to cancellation, but with non-thermal brightening. t 1 t 2 t 3 K. Harvey et al., 1999: TRACE; chromospheric,photospheric B LOS J. Chae et al., 1998: SUMER, BBSO magnetograms

8. Main Ideas 0. The transport of magnetic flux across the photosphere – emergence & submergence – plays a key role in many types of solar activity. Filament formation (flux cancellation), CME/flare triggering, the global dynamo, time-dependent coronal magnetic field models. 1. Flux only emerges & submerges along polarity inversion lines (PILs), along which B n vanishes. Vertical velocities elsewhere either: (1) are siphon flows, or (2) transport photospheric flux, but do not add or remove it. 2. Near disk center, the time-averaged Doppler shift determines the normal velocity, v n, hence whether flux is emerging or submerging. This shift is hard to determine – line center is pseudo- red-shifted relative to non-magnetic Sun. 3. If the horizontal field B h is known, the rate of flux emergence/ submergence along PILs can be quantified, v n B h. Pilot study soon, then to a review panel near you… Collaborators welcome!

9. Flows, v, affect magnetic evolution at both the surface and in the corona. Since E = -(v x B)/c + R, the fluxes of magnetic energy & helicity across the surface depend upon v. ∂ t U = c ∫ dA (E x B) ∙ n / 4π(1) ∂ t H = c ∫ dA (E x A) ∙ n / 4π(2) B in the corona is coupled to B at the surface, so the surface v provides an essential boundary condition for data-driven MHD simulations of the coronal B field. Flux emergence & submergence rates can constrain dynamo models. How much flux submerges during each cycle?

10. Doppler shifts don’t determine v away from PILs. Generally, Doppler shifts cannot distinguish flows || to B (red), perp. to B (blue), or in an intermediate direction (gray). With v  estimated another way & projected onto the LOS, the Doppler shift determines v || (Georgoulis & LaBonte, 2006) Doppler shifts are only unambiguous along polarity inversion lines, where B n changes sign (Chae et al. 2004, Lites 2005). v LOS

11. Photosphere Corona Siphon flows yield Doppler shifts, and change sign across PILs. Since they are parallel to B, they do not transport flux. Emergence should yield a DC Doppler shift along the PIL, and perhaps drain- ing flows near the PIL. There might be a net flow along the tube, from leading to following polarity (Fan et al.). L.O.S.

12. Photosphere Corona Perpendicular flows can transport flux, but away from PILs they do not add or remove flux from the photosphere. Submergence also occurs along PILs, and removes flux from the photosphere. L.O.S.

13. Tracking measures the apparent flux transport vel- ocity, u f, but can’t distinguish vertical & horizontal flows. u f is not equivalent to v; rather, u f  v hor - (v n /B n )B hor u f is the apparent velocity (2 components) v is the actual plasma velocity (3 comps) (NB: non-ideal effects can also cause flux transport!) Démoulin & Berger (2003): In addition to horizontal flows, vertical velocities can lead to u f  0. In this figure, v hor = 0, but v n  0, so u f  0.

14. Main Ideas 0. The transport of magnetic flux across the photosphere – emergence & submergence – plays a key role in many types of solar activity. Filament formation (flux cancellation), CME/flare triggering, the global dynamo, time-dependent coronal magnetic field models. 1. Flux only emerges & submerges along polarity inversion lines (PILs), along which B n vanishes. Vertical velocities elsewhere either: (1) are siphon flows, or (2) transport photospheric flux, but do not add or remove it. 2. Near disk center, the time-averaged Doppler shift determines the normal velocity, v n, hence whether flux is emerging or submerging. This shift is hard to determine – line center is pseudo- red-shifted relative to non-magnetic Sun. 3. If the horizontal field B h is known, the rate of flux emergence/ submergence along PILs can be quantified, v n B h. Pilot study soon, then to a review panel near you… Collaborators welcome!

15. These cartoons are simplistic; finding the absolute zero-Doppler level is hard, as there’s a pseudo-redshift. P. Scherrer (private communication): “… suppression of convective motions in magnetic regions as compared to non-magnetic regions, where there is a brightness - velocity correlation … [so] a blue shift where fields are not... It means it will be very model dependent to pick out radial velocity in magnetic vs non magnetic pixels. Does not mean it will not be a useful thing to do. Just that nothing is easy.” Pseudo-redshift is of order ~ 1 m/s per gauss (Scherrer, unpublished).

16. Main Ideas 0. The transport of magnetic flux across the photosphere – emergence & submergence – plays a key role in many types of solar activity. Filament formation (flux cancellation), CME/flare triggering, the global dynamo, time-dependent coronal magnetic field models. 1. Flux only emerges & submerges along polarity inversion lines (PILs), along which B n vanishes. Vertical velocities elsewhere either: (1) are siphon flows, or (2) transport photospheric flux, but do not add or remove it. 2. Near disk center, the time-averaged Doppler shift determines the normal velocity, v n, hence whether flux is emerging or submerging. This shift is hard to determine – line center is pseudo- red-shifted relative to non-magnetic Sun. 3. If the horizontal field B h is known, the rate of flux emergence/ submergence along PILs can be quantified, v n B h. Pilot study soon, then to a review panel near you… Avoid becoming a reviewer – become a collaborator!

17. What are some observations that have been reported recently?

18. Dopplergrams are sometimes consistent with siphon flows moving along the magnetic field. Left: MDI Dopplergram at 19:12 UT on 2003 October 29 superposed with the magnetic neutral line. Right: Evolution of the vertical shear flow speed calculated in the box region of the left panel. The two vertical dashed lines mark the beginning and end of the X10 flare. (From Deng et al. 2006) shear = “difference between the mean downflow and upflow speeds” Change of Doppler sign across PIL implies siphon flows along field lines that arch over PIL. Net “shear” implies DC Doppler shift (which the flare alters slightly).

19. Chae, Moon, & Pevtsov (2004) looked at two cancelling magnetic features in ASP data. CMF A CMF B

20. They found line shifts in Stokes’ I, Q, and U. Did they account for pseudo-redshift? Maybe not! CMF BCMF A

21. They found the rate of loss of normal flux,   /  t, matched B t v LOS. This is consistent with submergence, assuming the magnetic evolution is governed by the ideal magnetic induction equation. Measurements of flux changes vs. v z |B h | can reveal whether flux emergence / submergence is typically ideal or not.

22. Main Ideas 0. The transport of magnetic flux across the photosphere – emergence & submergence – plays a key role in many types of solar activity. Filament formation (flux cancellation), CME/flare triggering, the global dynamo, time-dependent coronal magnetic field models. 1. Flux only emerges & submerges along polarity inversion lines (PILs), along which B n vanishes. Vertical velocities elsewhere either: (1) are siphon flows, or (2) transport photospheric flux, but do not add or remove it. 2. Near disk center, the time-averaged Doppler shift determines the normal velocity, v n, hence whether flux is emerging or submerging. This shift is hard to determine – line center is pseudo- red-shifted relative to non-magnetic Sun. 3. If the horizontal field B h is known, the rate of flux emergence/ submergence along PILs can be quantified, v n B h. Pilot study soon, then to a review panel near you… Avoid becoming a reviewer – become a collaborator!